Appendices
Group 34
PART 1 : Figure 1.1: Summary Ouput - Initial Model
##
## Call:
## lm(formula = cmRate ~ medianAge + pctPoverty + pctBach + rmRace,
## data = cancer_mortality_rates)
##
## Residuals:
## Min 1Q Median 3Q Max
## -100.963 -13.973 1.864 13.971 112.002
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 181.8395 15.4857 11.742 < 2e-16 ***
## medianAge 0.0216 0.2258 0.096 0.924
## pctPoverty 0.9730 0.2260 4.306 1.98e-05 ***
## pctBach -1.7385 0.2404 -7.233 1.66e-12 ***
## rmRacewhite 3.2094 6.7514 0.475 0.635
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 23.97 on 532 degrees of freedom
## Multiple R-squared: 0.2358, Adjusted R-squared: 0.2301
## F-statistic: 41.05 on 4 and 532 DF, p-value: < 2.2e-16Figure 1.2: Residuals Plot - Initial Model
Figure 1.3: QQ Plot of Residuals - Initial Model
Figure 1.4: Histogram - Initial Model (with a log transformation)
Figure 1.5: Scatterplot Matrix of Data - Initial Model
Figure 1.6: Scatterplot - Initial Model
PART 2 : Figure 2.1 : Summary Ouput - Updated Model 1 (with log transformation)
##
## Call:
## lm(formula = cmRate ~ medianAge + log(pctPoverty) + log(pctBach) +
## rmRace, data = cancer_mortality_rates)
##
## Residuals:
## Min 1Q Median 3Q Max
## -95.644 -13.381 1.875 13.676 112.971
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 197.38383 23.71322 8.324 7.23e-16 ***
## medianAge 0.05195 0.21954 0.237 0.813030
## log(pctPoverty) 14.76224 3.88662 3.798 0.000163 ***
## log(pctBach) -24.23113 3.40192 -7.123 3.45e-12 ***
## rmRacewhite -0.32411 6.44839 -0.050 0.959933
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 23.88 on 532 degrees of freedom
## Multiple R-squared: 0.2419, Adjusted R-squared: 0.2362
## F-statistic: 42.43 on 4 and 532 DF, p-value: < 2.2e-16Figure 2.2: Residuals plot - Updated Model 1
Figure 2.3: QQ Plot of Residuals - Updated Model1
PART 3 : Figure 3.1: Scatterplot with Color - Initial Model
PART 4 : Figure 4.1 Updated Model 2 (remove rmRace and add region)
##
## Call:
## lm(formula = cmRate ~ medianAge + pctPoverty + pctBach + region,
## data = cancer_mortality_rates)
##
## Residuals:
## Min 1Q Median 3Q Max
## -82.645 -12.598 0.785 13.324 114.984
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 185.681713 12.265156 15.139 < 2e-16 ***
## medianAge 0.009403 0.218698 0.043 0.965723
## pctPoverty 0.655445 0.216710 3.025 0.002611 **
## pctBach -1.517447 0.236462 -6.417 3.08e-10 ***
## regionNortheast 3.223576 3.634499 0.887 0.375515
## regionSoutheast 10.575464 2.680767 3.945 9.06e-05 ***
## regionSouthwest -7.533614 3.753246 -2.007 0.045234 *
## regionWest -13.557700 3.605283 -3.761 0.000188 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 22.83 on 529 degrees of freedom
## Multiple R-squared: 0.3106, Adjusted R-squared: 0.3015
## F-statistic: 34.06 on 7 and 529 DF, p-value: < 2.2e-16Figure 4.2: Residuals Plot - Updated Model2
Figure 4.3: QQ Plot of Residuals - Updated Model2
Figure 4.4: Scatterplot with Color - Updated Model2
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
Figure 4.5: Interaction - Updated Model2
##
## Call:
## lm(formula = cmRate ~ medianAge + pctPoverty + pctBach + region,
## data = cancer_mortality_rates)
##
## Residuals:
## Min 1Q Median 3Q Max
## -82.645 -12.598 0.785 13.324 114.984
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 185.681713 12.265156 15.139 < 2e-16 ***
## medianAge 0.009403 0.218698 0.043 0.965723
## pctPoverty 0.655445 0.216710 3.025 0.002611 **
## pctBach -1.517447 0.236462 -6.417 3.08e-10 ***
## regionNortheast 3.223576 3.634499 0.887 0.375515
## regionSoutheast 10.575464 2.680767 3.945 9.06e-05 ***
## regionSouthwest -7.533614 3.753246 -2.007 0.045234 *
## regionWest -13.557700 3.605283 -3.761 0.000188 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 22.83 on 529 degrees of freedom
## Multiple R-squared: 0.3106, Adjusted R-squared: 0.3015
## F-statistic: 34.06 on 7 and 529 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = cmRate ~ medianAge + pctPoverty + pctBach + region +
## region * medianAge, data = cancer_mortality_rates)
##
## Residuals:
## Min 1Q Median 3Q Max
## -83.025 -12.426 1.066 13.263 119.994
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 225.4976 16.9377 13.313 < 2e-16 ***
## medianAge -0.9096 0.3559 -2.556 0.010869 *
## pctPoverty 0.6485 0.2158 3.005 0.002781 **
## pctBach -1.6070 0.2361 -6.806 2.75e-11 ***
## regionNortheast -24.9000 37.2851 -0.668 0.504536
## regionSoutheast -23.3533 21.4470 -1.089 0.276704
## regionSouthwest -84.5602 29.1778 -2.898 0.003911 **
## regionWest -96.7608 23.2354 -4.164 3.65e-05 ***
## medianAge:regionNortheast 0.6767 0.8901 0.760 0.447398
## medianAge:regionSoutheast 0.8012 0.5158 1.553 0.120971
## medianAge:regionSouthwest 1.9233 0.7394 2.601 0.009555 **
## medianAge:regionWest 2.0077 0.5538 3.625 0.000317 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 22.58 on 525 degrees of freedom
## Multiple R-squared: 0.3308, Adjusted R-squared: 0.3168
## F-statistic: 23.6 on 11 and 525 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = cmRate ~ medianAge + pctPoverty + pctBach + region +
## region * pctPoverty, data = cancer_mortality_rates)
##
## Residuals:
## Min 1Q Median 3Q Max
## -83.013 -12.717 1.336 12.913 109.817
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 172.35338 13.54165 12.728 < 2e-16 ***
## medianAge -0.04439 0.21822 -0.203 0.838886
## pctPoverty 1.78297 0.47566 3.748 0.000198 ***
## pctBach -1.49394 0.23702 -6.303 6.19e-10 ***
## regionNortheast 18.72030 13.20697 1.417 0.156943
## regionSoutheast 25.30363 8.19235 3.089 0.002117 **
## regionSouthwest 17.14721 13.39397 1.280 0.201034
## regionWest 25.50834 11.71214 2.178 0.029855 *
## pctPoverty:regionNortheast -1.15373 1.00337 -1.150 0.250726
## pctPoverty:regionSoutheast -1.10246 0.51640 -2.135 0.033231 *
## pctPoverty:regionSouthwest -1.67496 0.79136 -2.117 0.034767 *
## pctPoverty:regionWest -2.66706 0.75429 -3.536 0.000442 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 22.63 on 525 degrees of freedom
## Multiple R-squared: 0.3278, Adjusted R-squared: 0.3137
## F-statistic: 23.27 on 11 and 525 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = cmRate ~ medianAge + pctPoverty + pctBach + region +
## region * pctBach, data = cancer_mortality_rates)
##
## Residuals:
## Min 1Q Median 3Q Max
## -83.400 -12.271 0.917 13.144 115.606
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 187.52950 13.01787 14.406 < 2e-16 ***
## medianAge -0.02629 0.21984 -0.120 0.90487
## pctPoverty 0.57785 0.22148 2.609 0.00934 **
## pctBach -1.46626 0.37829 -3.876 0.00012 ***
## regionNortheast -7.09326 12.08534 -0.587 0.55750
## regionSoutheast 17.19739 6.87732 2.501 0.01270 *
## regionSouthwest -14.32425 11.43049 -1.253 0.21070
## regionWest -16.29305 11.31211 -1.440 0.15037
## pctBach:regionNortheast 0.59556 0.71720 0.830 0.40670
## pctBach:regionSoutheast -0.54389 0.48873 -1.113 0.26627
## pctBach:regionSouthwest 0.54405 0.82515 0.659 0.50997
## pctBach:regionWest 0.16842 0.69081 0.244 0.80748
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 22.83 on 525 degrees of freedom
## Multiple R-squared: 0.3161, Adjusted R-squared: 0.3017
## F-statistic: 22.06 on 11 and 525 DF, p-value: < 2.2e-16PART 5 (Final Model) : Figure 5.1
lm_final <- lm(cmRate ~ medianAge + log(pctPoverty) + log(pctBach) + region + medianAge * region + log(pctPoverty) * region, data = cancer_mortality_rates)
summary(lm_final)##
## Call:
## lm(formula = cmRate ~ medianAge + log(pctPoverty) + log(pctBach) +
## region + medianAge * region + log(pctPoverty) * region, data = cancer_mortality_rates)
##
## Residuals:
## Min 1Q Median 3Q Max
## -80.813 -12.483 1.388 12.908 115.309
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 197.0484 27.0751 7.278 1.26e-12 ***
## medianAge -0.7709 0.3517 -2.192 0.02883 *
## log(pctPoverty) 23.8175 6.4767 3.677 0.00026 ***
## log(pctBach) -20.1774 3.4251 -5.891 6.89e-09 ***
## regionNortheast 19.9793 49.2747 0.405 0.68530
## regionSoutheast 10.8963 31.1692 0.350 0.72679
## regionSouthwest -32.4127 46.0680 -0.704 0.48201
## regionWest -29.5334 46.3600 -0.637 0.52438
## medianAge:regionNortheast 0.5759 0.8891 0.648 0.51748
## medianAge:regionSoutheast 0.7103 0.5174 1.373 0.17038
## medianAge:regionSouthwest 1.8181 0.7393 2.459 0.01424 *
## medianAge:regionWest 1.7963 0.5690 3.157 0.00169 **
## log(pctPoverty):regionNortheast -16.1591 12.4488 -1.298 0.19485
## log(pctPoverty):regionSoutheast -12.1815 7.7235 -1.577 0.11535
## log(pctPoverty):regionSouthwest -18.0939 12.4148 -1.457 0.14559
## log(pctPoverty):regionWest -22.5391 13.0483 -1.727 0.08469 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 22.55 on 521 degrees of freedom
## Multiple R-squared: 0.3379, Adjusted R-squared: 0.3189
## F-statistic: 17.73 on 15 and 521 DF, p-value: < 2.2e-16Figure 5.2: Residuals Plot - final Model
Figure 5.3: QQ Plot of Residuals - Final Model
Figure 5.4: VIF - Final Model
## medianAge log(pctPoverty) log(pctBach)
## 1.111866 1.701780 1.672570Final Model - CMF
\(E(Y_{cmRate}|X) = \beta_0 + \beta_1 X_{medianAge} + \beta_2 log(X_{pctPoverty}) + \beta_3 log(X_{pctBach}) + \beta_4 I_{Northeast} + \beta_5 I_{Southeast} + \beta_6 I_{Southwest} + \beta_7 I_{West} + \beta_8 I_{Northeast} * X_{medianAge} + \beta_9 I_{Southeast} * X_{medianAge} + \beta_{10} I_{Southwest} * X_{medianAge} + \beta_{11} I_{West} * X_{medianAge} + \beta_{12} I_{Northeast} * log(X_{pctPoverty}) + \beta_{13} I_{Southeast} * log(X_{pctPoverty}) + \beta_{14} I_{Southwest} * log(X_{pctPoverty}) + \beta_{15} I_{West} * log(X_{pctPoverty})\)